
For any \(\alpha =(\alpha _1^\top , \alpha _2^\top , \alpha _3^\top , \alpha _4^\top )^\top \in \mathbb {R^+}^{4p_n}\) , \(h(\alpha )\)  is a lower bound to the optimality problem (REF ) (see [1]}). To find the best lower bound comes to solve the dual problem: \(\max _{\alpha \ge {\mathbf {0}}} h(\alpha ).\)
